O-LevelMathematicsProbability4024/12 · Oct/Nov 2016 · Q183 Marks

Four cards are marked with the numbers 1, 2, 3 and 4. One card is chosen at random. A second card is then chosen, at random, from the remaining three cards. The sum of the numbers on the two chosen cards is calculated.

(a)Complete the table to show the possible outcomes. First card Second card | | 1 | 2 | 3 | 4 --|---|---|---|--- 1 | | | | 2 | | | | 3 | | | | 4 | | | | [1]
(b)What is the probability that the sum is less than 2?[1]
(c)What is the probability that the sum is greater than 5?[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

[1] (a) [Table showing sums, with diagonals (self-pairings) marked as dash/shaded, and sums filled: (1,2)=3, (1,3)=4, (1,4)=5, (2,1)=3, (2,3)=5, (2,4)=6, (3,1)=4, (3,2)=5, (3,4)=7, (4,1)=5, (4,2)=6, (4,3)=7]
[1] (b) 0
[1] (c) 4/12 oe ; or FT their table

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